Question

A new purification unit is installed in a chemical process. Before its installation, a random sample yielded the following data about the percentage of impurity: ?̅̅1̅ = 9.85, ?1 2 = 6.79 and ?1 = 10. After installation, a random sample resulted in ?̅̅2̅ = 8.08, ?2 2 = 6.18 and ?2 = 8. a. Can you conclude that the two variances are equal? Use α = 0.05. b. Can you conclude that the new purification device has reduced the mean percentage of impurity? Use α = 0.05.

Answer 1

ANSWER:

Given that:

A new purification unit is installed in a chemical process.

Before its installation, a random sample yielded the following data about the percentage of impurity: ?̅̅1̅ = 9.85, ?1 2 = 6.79 and ?1 = 10.

After installation, a random sample resulted in ?̅̅2̅ = 8.08, ?2 2 = 6.18 and ?2 = 8.

a)

  Can you conclude that the two variances are equal

here Fstat =S1²/s2² =(6.79/6.18)=1.098

from excel for above F stat p value =2*fdist(1.098,9,7)=2*0.46=0.92

as p vlaue is higher then 0.05 level; hence we can not reject that 2 variance are equal.

b)

  Can you conclude that the new purification device has reduced the mean percentage of impurity

as we consider that 2 means are equal;

here degree of freedom =n1+n2-2 =16

pooled std deviation =((n1-1)S1²+(n2-1)s2²)/(n1+n2-2))^1/2 =2.554

for std error =Sp(1/n1+1/n2)^1/2 =1.2115

hence test stat =(X1-X2)/std error =(9.85-8.08)/1.2115=1.460

for above p value =tdist(1.460,16,1)=0.0817

as p vlaue is greater then 0.05 level; hence we can not conclude that mean has reduced